Subgroups — #16817540

Order 3712.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271543	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#90768	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₆	—	2	1	no	—
5	C₂×Dic₁₁₆	C₄	1	2	yes	—
6	#11745231	—	2	1	no	—
7	C₂₉×C₄⋊C₈	—	2	1	no	—
8	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×#90768	—	2	1	no	—
10	C₂×Dic₅₈	—	2	2	no	—
11	C₂×C₈×C₂₉	—	4	1	no	—
12	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₄²×C₂₉	D₄	1	1	yes	characteristic
15	C₄⋊Dic₂₉	—	4	1	no	—
16	C₄⋊Dic₂₉	—	4	1	no	—
17	Dic₁₁₆	—	4	2	no	—
18	Dic₁₁₆	—	4	1	no	—
19	Dic₁₁₆	—	4	1	no	—
20	#90768	—	4	1	no	—
21	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
23	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
24	C₂×Dic₂₉	—	4	2	no	—
25	Dic₅₈	—	4	2	no	—
26	Dic₅₈	—	4	2	no	—
27	C₈×C₂₉	—	2	1	no	—
28	C₈×C₂₉	—	8	1	no	—
29	C₈×C₂₉	D₈	1	1	yes	characteristic
30	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
31	#1362	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	#102	1	1	yes	characteristic
33	C₄×C₂₉	—	2	1	no	—
34	C₄×C₂₉	#100	1	1	yes	characteristic
35	C₄×C₂₉	#102	1	1	yes	characteristic
36	C₄×C₂₉	SD₃₂	1	1	yes	characteristic
37	C₄×C₂₉	Q₃₂	1	1	yes	characteristic
38	Dic₂₉	—	8	2	no	—
39	#494	—	29	1	no	—
40	C₄⋊C₁₆	—	29	1	no	—
41	#335	D₂₉	1	1	yes	characteristic
42	C₂×C₂₉	#331	1	1	yes	characteristic
43	C₂×C₂₉	#358	1	1	yes	characteristic
44	C₂×C₂₉	#362	1	1	yes	characteristic
45	C₂×Q₁₆	—	29	2	no	—
46	C₂×Q₁₆	—	58	1	no	—
47	C₄⋊Q₈	—	58	1	no	—
48	C₂×C₁₆	—	58	1	no	—
49	C₄⋊C₈	—	2	1	no	—
50	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
51	C₂₉	#1362	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	58	2	no	—
53	Q₁₆	—	116	2	no	—
54	Q₁₆	—	116	1	no	—
55	Q₁₆	—	116	1	no	—
56	C₂×C₈	—	4	1	no	—
57	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
58	C₂×C₈	D₁₁₆	1	1	yes	characteristic
59	C₄⋊C₄	—	116	1	no	—
60	C₄⋊C₄	—	116	1	no	—
61	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
62	C₁₆	—	116	1	no	—
63	Q₈	—	116	2	no	—
64	Q₈	—	116	2	no	—
65	C₂×C₄	—	116	2	no	—
66	C₂×C₄	#90781	1	1	yes	characteristic
67	C₂×C₄	#90782	1	1	yes	characteristic
68	C₂×C₄	#90784	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	8	1	no	—
71	C₈	#90773	1	1	yes	characteristic
72	C₈	D₂₃₂	1	1	yes	characteristic
73	C₂²	#11745157	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	232	2	no	—
76	C₄	#11745169	1	1	yes	characteristic
77	C₄	#11745171	1	1	yes	characteristic
78	C₄	#11745175	1	1	yes	characteristic
79	C₄	#11745177	1	1	yes	characteristic
80	C₂	#14270906	1	1	yes	characteristic
81	C₂	#14270966	1	1	yes	characteristic
82	C₂	#14270978	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745157
commutator	C₂×C₈×C₂₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#335	C₂
socle, prime radical	C₂²×C₂₉	#102
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#335	D₂₉
hypocenter	C₂₉	#1362
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
51. C₂₉	#1362	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14271543	2
C₄⋊#90768	2
C₂₉×#335	2
#1362	29